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On the joint distribution of runs in the sequence of Markov-dependent multi-state trials

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  • Shinde, R.L.
  • Kotwal, K.S.

Abstract

Under different popular counting schemes of runs we have obtained probability-generating function (pgf) of the joint distribution of runs in a sequence of Markov-dependent multi-state trials. A method of conditional pgf's is used to obtain these joint distributions. Expanding the matrix polynomial of degree n, involved in the pgf, a recurrent formula for evaluation of exact probability distribution is obtained. To show the feasibility and compatibility of the results obtained, the joint distributions are numerically evaluated.

Suggested Citation

  • Shinde, R.L. & Kotwal, K.S., 2006. "On the joint distribution of runs in the sequence of Markov-dependent multi-state trials," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1065-1074, May.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:10:p:1065-1074
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    References listed on IDEAS

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    1. Sigeo Aki & Katuomi Hirano, 2000. "Numbers of Success-Runs of Specified Length Until Certain Stopping Time Rules and Generalized Binomial Distributions of Order k," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 767-777, December.
    2. Ling, K. D., 1988. "On binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 6(4), pages 247-250, March.
    3. Doi, Masayuki & Yamamoto, Eiji, 1998. "On the joint distribution of runs in a sequence of multi-state trials," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 133-141, August.
    4. Qing Han & Sigeo Aki, 1999. "Joint Distributions of Runs in a Sequence of Multi-State Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 419-447, September.
    5. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 743-766, December.
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    Cited by:

    1. Kirtee Kamalja, 2014. "On the joint distribution of success runs of several lengths in the sequence of MBT and its applications," Statistical Papers, Springer, vol. 55(4), pages 1179-1206, November.
    2. Xian Zhao & Yanbo Song & Xiaoyue Wang & Zhiyue Lv, 2022. "Distributions of $$({k}_{1},{k}_{2},\dots ,{k}_{m})$$ ( k 1 , k 2 , ⋯ , k m ) -runs with Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2689-2702, December.
    3. Yung-Ming Chang & James Fu & Han-Ying Lin, 2012. "Distribution and double generating function of number of patterns in a sequence of Markov dependent multistate trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 55-68, February.

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